Bilinear Optimal Control of an Advection-Reaction-Diffusion System

Bilinear Controllability of a Class of Advection-Diffusion-Reaction Systems

In this paper, we investigate the exact controllability properties of an advection-diffusion equation on a bounded domain, using timeand space-dependent velocity fields as the control parameters. This partial differential equation (PDE) is the Kolmogorov forward equation for a reflected diffusion process that models the spatiotemporal evolution of a swarm of agents. We prove that if a target pr...

Optimal Stretching in Advection-Reaction-Diffusion Systems.

We investigate growth of the excitable Belousov-Zhabotinsky reaction in chaotic, time-varying flows. In slow flows, reacted regions tend to lie near vortex edges, whereas fast flows restrict reacted regions to vortex cores. We show that reacted regions travel toward vortex centers faster as flow speed increases, but nonreactive scalars do not. For either slow or fast flows, reaction is promoted...

Optimal control of a diffusion/reaction/switching system

We consider an optimal control problem involving the use of bacteria for pollution removal where the model assumes the bacteria switch instantaneously between active and dormant states, determined by threshold sensitivity to the local concentration v of a diffusing critical nutrient; compare [7], [3], [6] in which nutrient transport is convective. It is shown that the direct problem has a solut...

Optimal Control and Numerical Adaptivity for Advection–diffusion Equations

We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the Lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error ...

Numerical Solution of Advection-Diffusion-Reaction Equations